2014/10/05 by Chuanming Zong, Zong, Chuanming
Engineering · #52C17 #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Packing Problems
paper · pdf · doi:10.48550/arxiv.1410.1102
openalex publication_date 2014/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Packings of identical objects have fascinated both scientists and laymen alike for centuries, in particular the sphere packings and the packings of identical regular tetrahedra. Mathematicians have tried for centuries to determine the densest packings; Crystallographers and chemists have been fascinated by the lattice packings for centuries as well. On the other hand, physicists, geologists, material scientists and engineers have been challenged by the mysterious random packings for decades. Experiments have shown the existence of the dense random sphere packings and the loose random sphere packings for more than half a century. However, a rigorous definition for them is still missing. The purpose of this paper is to review the random solid packings and to create a mathematical theory for it.